Need help on the steps to solving problem

**colorado** · Jan 6th 2011, 05:15 AM

I have this problem:

4/21=(3p-4)/7sqrt(p^2+20)

I could use a detail step through process for solving this. I know that p=4 or -44/65
I know that it comes downs to using the quadratic formula or factoring to solve the quadratic equation.

my steps so far have been

if 4/21=(3p-4)/7sqrt(p^2+20) then 4/21*7sqrt(p^2+20)=3p-4
next I get 28sqrt(p^2+20)/21=3p-4
then 4sqrt(p^2+20)/3=3p-4
then I multiple both sides be the LCD (3) to eliminate the fraction
I get 4sqrt(p^2+20)=9p-12)
then I need help from here so I fully understand
I know I need to square both sides and factor but I need to know all the steps
thank you!

**malaygoel** · Jan 6th 2011, 05:35 AM

since you have tried pretty well, here are the steps:

$4 \sqrt{p^2 + 20} = 9p-12$

squaring both sides

$16 (p^2 + 20)= {(9p-12)}^2$

$16p^2 +320 = 81p^2 - 216 p +144$

$16 p^2 - 81p^2 +216p +320-144=0$

$-65p^2 +216p +176=0$

$65p^2-216p-176=0$

can you take from here?

**colorado** · Jan 6th 2011, 05:40 AM

I can take it from there is I use the quadratic formula :

p=-b + or - sqrt b^2-4ac/2a

could you though explain how to factor it properly?

If I do (65p+22)(p-22) I don't get the answer but if I do (65p+44)(p-4) I do. but -8*22=-4*44

**rebghb** · Jan 6th 2011, 06:16 AM

Originally Posted by colorado

I can take it from there is I use the quadratic formula :

p=-b + or - sqrt b^2-4ac/2a

could you though explain how to factor it properly?

If I do (65p+22)(p-22) I don't get the answer but if I do (65p+44)(p-4) I do. but -8*22=-4*44

It's $p = \frac{-b-\sqrt{b^2 -4ac}}{2a}$ or $p = \frac{-b+\sqrt{b^2 -4ac}}{2a}$ .
Plugging in values for $a, b$ and $c$ , you'll get:
$p = 4$ or $p = -44/65$

**colorado** · Jan 6th 2011, 07:00 AM

thanks guys

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